lim _{x rightarrow 0} frac{x^2 2^x-x^2 sin x- | vedclass

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Question

(D) આપેલ લક્ષ: $\lim _{x \rightarrow 0} \frac{x^2(2^x - \sin x - 1)}{3^x(1 - \cos x) - (1 - \cos x)}$$= \lim _{x \rightarrow 0} \frac{x^2(2^x - \sin x

Vedclass · Accepted Answer

$\frac{2}{\log 3}(\log 2-1)$

Vedclass · Answer

(D) આપેલ લક્ષ: $\lim _{x \rightarrow 0} \frac{x^2(2^x - \sin x - 1)}{3^x(1 - \cos x) - (1 - \cos x)}$$= \lim _{x \rightarrow 0} \frac{x^2(2^x - \sin x - 1)}{(3^x - 1)(1 - \cos x)}$$= \lim _{x \rightarrow 0} \frac{2^x - \sin x - 1}{(3^x - 1) \frac{(1 - \cos x)}{x^2}}$કારણ કે $\lim _{x \rightarrow 0} \frac{1 - \cos x}{x^2} = \frac{1}{2}$,પદ આ મુજબ બને છે:$= \lim _{x \rightarrow 0} \frac{2(2^x - \sin x - 1)}{3^x - 1}$એલ-હોસ્પિટલના નિયમનો ઉપયોગ કરતા:$= \lim _{x \rightarrow 0} \frac{2(2^x \ln 2 - \cos x)}{3^x \ln 3}$$= \frac{2(\ln 2 - 1)}{\ln 3}$$= \frac{2}{\log 3}(\log 2 - 1)$

$\lim _{x \rightarrow 0} \frac{x^2 2^x-x^2 \sin x-x^2}{3^x+\cos x-3^x \cos x-1}=$

Similar Questions

લક્ષની કિંમત શોધો: $\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}$

$\mathop {\lim }\limits_{x \to 0} \frac{{x\cos x - \sin x}}{{{x^2}\sin x}} = $

ધારો કે $f: R \rightarrow R$ એ $x=0$ આગળ વિકલનીય છે. જો $f(0)=0$ અને $f'(0)=2$ હોય, તો $\lim _{x \rightarrow 0} \frac{1}{x} [f(x)+f(2 x)+f(3 x)+\ldots+f(2015 x)]$ ની કિંમત શોધો.

જો $f(0) = 2$ હોય,તો $\mathop {\lim }\limits_{x \to 0} \frac{{\int\limits_0^x {\left( {tf(x) + xf(t)} \right)dt} }}{{{x^2}}}$ ની કિંમત શોધો.

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